It's been pointed out that a minor Australian Sabbatarian ministry teaches that originally Islam was in some sense an embodiment of the Church of God. The leader of this group even goes as far as saying that Mohammad enjoined Sabbath observance, and that the Qur'an is a "commentary" on the Bible.
Clearly this is not what was implied in the recent AW post. In fact, in my opinion, it's complete rubbish. The Jewish Christians of Arabia certainly seem to have influenced Islam, but they were very different from what passes for the Church of God today, whether based in Cincinnati, Charlotte, Edmond or Canberra. In fact, if you do any reading on these Jewish Christian believers, you can't help but be struck by how different and strange they seem, rather than by the similarities.
The history of early Christianity is fascinating, but there is an awful lot we don't know. For example one scholar, Ray Pritz, contends that the group called Nazarenes were distinct from the Ebionites, and develops an apologetic reconstruction that must sit nicely with conservative, mainstream Christians. I don't buy that for a single moment (see Bob Price's review of the Pritz book.) The point is that history is often frustratingly fuzzy on the specifics. Sect leaders who turn speculation into dogma are not in the same business as cautious historians and scholars: let the buyer beware. How Jewish and Christian belief (along with Jewish-Christian belief) impacted on Islam may be an overlooked but interesting story, but how does that authorise, legitimate or lend credibility to any modern, unrelated Sabbatarian sect?
It doesn't. It does provide a lesson in humility, however, for those who want to use history as an ideological weapon in the service of doctrine.
All religions borrow from those that went before. Second Temple Judaism borrowed from Zoroastrianism (Satan, resurrections), early Christianity was as syncretistic as any other movement, Islam learned its monotheism in part from sectarian Christians and Jews, Herbert Armstrong raided the bottom drawers of Adventism, British-Israelism and the Mormons. And so it goes.